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http://dx.doi.org/10.5831/HMJ.2010.32.3.413

GENERAL TYPES OF (α,β)-FUZZY IDEALS OF HEMIRINGS  

Jun, Y.B. (Department of Mathematics Education, Gyeongsang National University)
Dudek, W.A. (Institute of Mathematics and Computer Science, Wroclaw University of Technology Wyb.)
Shabir, M. (Department of Mathematics, Quaid-i-Azam University)
Kang, Min-Su (Department of Mathematics, Hanyang University)
Publication Information
Honam Mathematical Journal / v.32, no.3, 2010 , pp. 413-439 More about this Journal
Abstract
W. A. Dudek, M. Shabir and M. Irfan Ali discussed the properties of (${\alpha},{\beta}$)-fuzzy ideals of hemirings in [9]. In this paper, we discuss the generalization of their results on (${\alpha},{\beta}$)-fuzzy ideals of hemirings. As a generalization of the notions of $({\alpha},\;\in{\vee}q)$-fuzzy left (right) ideals, $({\alpha},\;\in{\vee}q)$-fuzzy h-ideals and $({\alpha},\;\in{\vee}q)$-fuzzy k-ideals, the concepts of $({\alpha},\;\in{\vee}q_m)$-fuzzy left (right) ideals, $({\alpha},\;\in{\vee}q_m)$-fuzzy h-ideals and $({\alpha},\;\in{\vee}q_m)$-fuzzy k-ideals are defined, and their characterizations are considered. Using a left (right) ideal (resp. h-ideal, k-ideal), we construct an $({\alpha},\;\in{\vee}q_m)$-fuzzy left (right) ideal (resp. $({\alpha},\;\in{\vee}q_m)$-fuzzy h-ideal, $({\alpha},\;\in{\vee}q_m)$-fuzzy k-ideal). The implication-based fuzzy h-ideals (k-ideals) of a hemiring are considered.
Keywords
$({\alpha},\\in{\vee}q_m)$-fuzzy left (right) ideal; $({\alpha},\\in{\vee}q_m)$-fuzzy h (k)-ideal; fuzzifying left (right) ideal; fuzzifying h (k)-ideal; t-implication-based fuzzy left (right) ideal; t-implication-based fuzzy h (k)-ideal;
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